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Updated: May 12, 2025
As we approach the Croton River the road takes a right-angled turn, down which a fingerboard points, indicating that Peekskill lies that way, but the old Post Road kept straight ahead, following the banks of the Croton until a favorable place for crossing occurred, when it took advantage of the opportunity and started back for the Hudson, in order to get around Hessian Hill.
Further away, half-right, you can see Guillemont." "In that case," remarked Wagstaffe, "our right flank would appear to be strongly supported by the enemy." "Yes. We are in a sort of right-angled salient here. We have the enemy on our front and our right. In fact, we form the extreme right of the attacking front. Our left is perfectly secure, as we now hold Mametz Wood and Contalmaison.
Thus if you voluntarily produce the idea of a right-angled triangle, and then of a square; and after having excited these ideas repeatedly, you excite the idea of their difference, which is that of another right-angled triangle inverted over the former; you are said to reason upon this subject, or to compare your ideas.
They usually light it with mirrors made by hollowing the surface of an isosceles right-angled triangle, which conducts all the rays of light into one point.
Their mathematicians knew the rule for finding the area of a triangle from its sides, and also the celebrated proposition concerning the squares on the sides of the right-angled triangle. The Chinese, it is said, also knew this proposition before it was known to the Greeks, among whom it was first propounded by Thales. He applied a circle to the measurement of angles.
The following sentence, for instance, is devoid of style: "The square on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the other two sides": for, although by its content it conveys to the intellect a meaning which is entirely clear and absolutely definite, it does not by its sound convey to the senses a suggestion which is cognate.
It is within this right-angled triangular space that the battle, now proceeding, bids fair to rage most fiercely. They find the brigades of Bee, Bartow, and Evans, falling back in great disorder, and taking shelter in a wooded ravine, South of the Robinson House and of the Warrenton Pike.
The principles of it remained so foreign to me that I did not even recognise a right-angled triangle, if the right angle were uppermost.
Carpets were laid in strips, not tacked down to stay, and rugs were laid so as to show a goodly glimpse of hardwood floor; and in the dining-room a large, round table was placed instead of a right-angled square one. This table was not covered with a tablecloth; instead, mats and doilies were used here and there.
Jackson, however, is now hurrying up to the relief of the flying and disordered remnants of Bee's, Bartow's, and Evans's Brigades; and these subsequently rally, with Hampton's Legion, upon Jackson's strong brigade of fresh troops, so that, on a third new line, to which they have been driven back, they soon have 6,500 Infantry, 13 pieces of Artillery, and Stuart's cavalry-posted in a belt of pines which fringes the Southern skirt of the Henry House plateau in a line-of-battle which, with its left resting upon the Sudley road, three-quarters of a mile South of its intersection with the Warrenton Pike, is the irregular hypothenuse of a right-angled triangle, formed by itself and those two intersecting roads, to the South-East of such intersection.
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